You should just get some green fake fur. Run it through your washer, with no fabric softener, and it will come out rather 'ratty' looking. Let it air dry.. Another thing you could do with the fabric is to get a bottle of fabric stiffener at the craft...
There are several types of interfacing that can be attached to fabric to give it more structure. Some of them are ironed on while others are sewn onto the fabric. They can be found in the fabric section of stores.
You will find a lot of small pieces of fabric on Ebay, but the remnant bin in your local fabric store will give you the best choices. Also, don't be afraid to ask around to anyone you know who sews. People always have smaller pieces in their stash th...